Transition from non-Fickian to Fickian longitudinal transport through 3-D rough fractures: Scale-(in)sensitivity and roughness dependence

Abstract

Understanding transport in rough fractures from non-Fickian to Fickian regimes and the prediction of non-Fickian transport is critical for the development of new transport theories and many practical applications. Through computational experiments that fall within the macrodispersion regime, we first simulated and analyzed solute transport through synthetic rough fractures with stationary geometrical properties (i.e., fracture roughness σb/〈b〉 and correlation length λ, where b refers to aperture with its standard deviation σb and arithmetic mean 〈b〉) across increasing fracture longitudinal transport domain length L, with L/λ ranging from 2.5 to 50. The results were used to determine how solute transport behavior evolves with increasing scale in the longitudinal direction. Moreover, a set of correlated fractures with aperture fields following normal and log-normal distributions was created to further identify and quantify the dependence of non-Fickian transport on roughness. We found that although persistent intermittent velocity structures were present, the breakthrough curves (BTCs) and residence time distributions showed diminishing early arrival and tailing, features of non-Fickian transport, with increasing longitudinal L/λ, ultimately converging to a Fickian transport regime given σb/〈b〉 remained constant. Inverse analysis of the experimental BTCs with the advection-dispersion equation (ADE) model showed that the dispersion coefficient (D) was non-trivially scale-dependent. Simulation results for rough fractures with varying σb/〈b〉 and L/λ indicated that the ratio of fluid velocity to transport velocity fitted to the ADE model depends on σb/〈b〉 and L/λ. The continuous time random walk (CTRW) performed much better across all transport scales, and resulted in scale-independent fitted parameters, i.e., β in the memory function. The fitted β is proportional to σb/〈b〉but is insensitive to L/λ. Therefore, bulk longitudinal solute transport across the pre-asymptotic and asymptotic regimes can be estimated based on the CTRW model parameterized by measurable fracture physical properties.